| Microarray technology has been widely used to study gene expression in biological and medical research. cDNA microarrays have been standard equipments in biology laboratories. Methods for identifying differentially expressed genes are still evolving. In cDNA microarray experiments, fluorescent intensities are subject to numerous sources of variation. These variations have to be removed so that the real difference in gene expression in the different kinds of cells or tissues can be detected. The currently widely used method involves background correction, log-transformation, and normalization of the measured intensities. the most popular data transformation is log-ratio transformation, i.e. log-transformation of the ratio of the background-corrected intensity of one mRNA sample to that of the other sample. Normalization calibrates the signals from different channels and arrays to a comparable scale. Although the log-ratio transformation approach (referred to as the "log-ratio approach" hereafter) has been widely used in cDNA microarray data analysis, it has some problems, as point out by Huber et al.: If a gene is expressed weakly or not at all, it may happen by chance that the background-corrected foreground intensities become negative. However, non-positive values do not make sense for either ratios or log-transformation. And normalization requires a assumption that only a relatively small proportion of the genes are differentially expressed in the two mRNA samples, and that there is symmetry in the expression of the up-regulated/down-regulated genes. If these assumptions do not hold, which happens in many cases, the estimates of the "noise" effects will be biased.We proposed a normalization method using a variance ratio discriminant according to the method proposed by Rocke and Durbin. The factors of influencing normalization were simulated in this study. The results showed that (1) a was always overestimated, but relative deviation was at a low level. That means background influence can be corrected effectively. (2) E(e~η) is estimated more accurate, and relative deviation was under 0.5%. (3) Those differentially expressed genes had little influence on the estimation of β_i when only a relatively small proportion of the genes are differentially expressed in the two mRNA samples. This normalization method can partly solve the problems with the log-ratio transformation. But its application was limited because of the requirement in the experiment design and gene components. Meanwhile we found when the proportion of the differentially expressed genes in the two mRNA samples is relative high (e.g. 30%) and there is not symmetry in the expression of the up/down-regulated genes, it is hard to eliminate the "noise" effectively.In view of the problems, we modified the normalization formula and the discriminant (for simplicity, call it the "non-transformation approach"). We take use of a t-statistic as a discriminant that can eliminate the potential differentially expressed genes so that it can improve the veracity of the parameters estimation. The results showed that this approach was feasible and performed better than the current popular log-ratio approach in all cases investigated. That means that non-transformation approach solved the problems with log-ratio approach. It can eliminate "noise" in the experiments, andcan identify more genes than log-transformation method with low level of false discovery rate. Specially, when the proportion of the differentially expressed genes in the two mRNA samples is relative high (e.g. 30%) and there is not symmetry in the expression of the up/down-regulated genes, it still works well. Real cDNA microarray data in the Apo Alexperiment were analyzed to test the feasibility and efficiency of this approach for detecting differentially expressed genes. The results showed that our approach worked well and can identify more genes than log-transformation method. Therefore, it could be an alternative method for analyzing cDNA microarray data.
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